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APMO 1989

Posted: Mon Apr 09, 2012 9:16 pm
by nafistiham
How to crack this one ?

Prove that the equation
\[6(6a^2 + 3b^2 + c^2) = 5n^2\]
has no solutions in integers except $a = b = c = n = 0$.

Re: APMO 1989

Posted: Mon Apr 09, 2012 9:43 pm
by nayel
The first thing that came to my mind after seeing $3,6$ and the squares is
infinite descent/extreme principle/consider minimum solution - whatever you want to call it.
It should work I believe.

Re: APMO 1989

Posted: Mon Feb 04, 2019 6:28 pm
by samiul_samin
nafistiham wrote:
Mon Apr 09, 2012 9:16 pm
How to crack this one ?

Prove that the equation
\[6(6a^2 + 3b^2 + c^2) = 5n^2\]
has no solutions in integers except $a = b = c = n = 0$.
Solved here.